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Exercise 6.10.6

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Let $x = (1, - 2, 3)$ . First compute that

R (x) = \frac{⟨ Bx, x ⟩}{∥ x ∥^{2}}

= \frac{⟨ (3, 0, 5), (1, - 2, 3) ⟩}{14} = \frac{9}{7} .

Second, compute the eigenvalues of $B$ to be $4, 1, 1$ . Hence we have $∥ B ∥ = 4$ and $∥ B^{- 1} ∥ = 1^{- 1} = 1$ . Finally calculate the condition number to be

cond (B) = 4 \times 1 = 4 .

jephianlin

2011-06-27 00:00

Exercise 6.10.6

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